I am a member of a historically Jewish sorority, and I was also a founding sister of my chapter. In my chapter, we have lots of Jewish sisters, but also Catholics, Lutherans, Episcopals, Greek Orthodox, Hindus, etc. We didn't consider religion when making decisions as to whom to invite/bid; we considered whether each woman would make a good sister and what she'd bring to the sorority.
My chapter did have a bylaw forbidding the scheduling of mandatory events on the Sabbath and Jewish holidays (so all our formals were on Saturday nights), but that same bylaw also forbade scheduling events on the major holidays of any other religion that a sister practiced.
So, go for it.
Every new colony needs leaders, and it sounds like you'd be a good one.
Which sorority, and which school?